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A POSSIBLE EXOTIC BARYON RESONANCE

Written November 2003 by G. Trilling (LBNL).

I. Introduction

The well-established baryon states can be understood as

combinations of three valence quarks. In this discussion, we

confine ourselves to baryon states constructed from combina-

tions of u, d, and s quarks. The three-quark combinations are

members of SU(3) singlets, octets, and decuplets. Baryon states

that cannot be constructed with triplets of u, d, and s quarks

are called exotic.

Do there exist in nature baryon states constructed from

more complicated quark configurations? The simplest might

consist of four quarks plus an antiquark. In a 1997 paper [1],

Diakonov et al. proposed, on the basis of a chiral soliton model,

the existence of a low-mass anti-decuplet of such baryons, with

spin 1/2 and even parity, and with specific estimates for the

masses and widths. Figure 1, from their paper, shows this

proposed anti-decuplet. The baryons at the three corners of

the triangle are exotic: their isospin and strangeness cannot be

obtained by any triplet combination of u, d, and s quarks. The

other baryons of the anti-decuplet are made up of combinations

such as, for example, uuddd and uudss (relevant to the charged

N(1710) in Fig. 1). These two combinations have the same

isospin and strangeness as uud, and the corresponding baryons

are therefore not exotic. Diakonov et al. estimated the masses

and widths of the four isospin multiplets in the anti-decuplet of

Fig. 1. They assumed equal mass spacings between multiplets,

with a calculated spacing of 180 MeV. Associating the S = 0

isospin doublet with the N(1710), an I = J = 1/2, P -wave πN

resonance listed in our Tables, they predicted a mass of 1530

MeV for the S = +1 exotic Z+ isosinglet. They also estimated

its total decay width to be 15 MeV or less.

Before 2003, there was no evidence for a narrow S = +1

baryon resonance, but that situation has now changed. In 2003,

several groups searched old or new data for evidence of a

K+n or K0p resonance in the neighborhood of the predicted

1530 MeV and reported positive results. On the other hand,

CITATION: S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004) (URL: http://pdg.lbl.gov)

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Figure 1: Proposed anti-decuplet of baryons(from [1]).

attempts to find this exotic state in other fairly extensive older

published data have so far yielded no supporting evidence. We

first consider the new positive results, and then review some of

the relevant older information. One point of nomenclature: the

Z+ is now universally called the Θ+.

II. Recent results

We discuss the results from seven different experiments.

Five are photo- or electroproduction experiments using carbon,

deuterium, or hydrogen targets, one is a K+n charge-exchange

experiment in a liquid-xenon bubble chamber, and one involves

a compilation of neutrino bubble-chamber data with hydrogen,

deuterium, and neon fills. As an example, we show in Fig. 2

the nK+ mass spectrum from the first of two CLAS pho-

toproduction experiments discussed below [2]. The structure

at 1540 MeV is interpreted as a possible Θ+ signal with a

significance of 5.2 σ.

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Figure 2: Invariant nK+ mass spectrum fromthe reaction γd → K+K−pn after cuts. Thedotted histogram shows events associated withΛ(1520) → K−p production (from [2]).

The LEPS experiment — The LEPS experiment [3] was

carried out at the Laser-Electron-Photon facility at the Spring-

8 Synchrotron Radiation Facility in Japan during 2000–2001. A

photon beam with tagged energies between 1.5 and 2.4 GeV was

incident on a scintillator target; for the Θ+ search, the reaction

γn → nK+K−, with carbon from the scintillator as the neutron

target, was identified and measured in the LEPS spectrometer.

The goal was to search for a nK+ mass enhancement. Cuts

were made to remove a large number of φ → K+K− decays

and possible backgrounds from γp → pK+K− in the same

carbon target. Corrections were made for the Fermi momentum

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of the target nucleon, relevant to the reconstruction since the

final-state neutron is not detected. After cuts, the final sample

consists of 109 events. There is a peak at 1540 MeV, consisting

of 19 events above a background of 17. The significance is

claimed to be 4.6 σ, the mass 1540 ± 10 MeV, and the width

less than 25 MeV at 90% confidence.

The DIANA experiment — The DIANA experiment [4], run

in 1986, was a xenon bubble-chamber exposure to a K+ beam.

The K+ momentum at the bubble-chamber entry was 750

MeV/c, decreasing through ionization loss all the way to rest

at the back of the chamber. Only those interactions produced

by K+ of momenta below 550 MeV/c were considered in the

analysis, which focused on charge-exchange events, K+Xe →

K0SpX , with the K0

S decaying into π+π−. After cuts to remove

low-momentum protons and K0S, and cuts on K0

S and proton

directions (said to reduce the effects of rescatterings in nuclear

matter), a sharp peak in the pK0S mass spectrum at 1539 ± 2

MeV, consisting of a signal of 29 events over a background of

44 events, was observed. The quoted statistical significance is

4.4 σ, and the width upper limit is 9 MeV.

The CLAS experiments — The first of the CLAS experi-

ments [2], run in 1999 at Jefferson Lab, studied the nK+ mass

spectrum from the reaction γd → npK+K−, produced by a

tagged photon beam of energies between 1.5 and 2.9 GeV. The

events of interest are really γn → nK+K−, but reconstruc-

tion requires a detectable proton; hence only events with a

rescattering that changes the spectator into a detectable proton

are useful. With removal of φ → K+K− and Λ(1520) → pK−

events, and an imposed upper limit of 1 GeV/c on the K+

momentum, the spectrum shown in Fig. 2, with a signal of 43

events over a background of about 54 events, is observed. The

mass is 1542± 5 MeV, the quoted significance is 5.2 σ, and the

observed width of 21 MeV is consistent with the instrumental

resolution.

Another CLAS experiment [5] studied the reaction γp →

nπ+K+K−, a four-body final state, with photons of energies

between 3 and 5.5 GeV. After a φ mass cut, the nK+ mass

distribution for 14,000 events shows no significant structure.

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To enrich the sample, angular requirements that select events

with forward π+ and backward K+ are imposed. These cuts

remove about 95% of the events, leaving a peak in the nK+

mass at 1555± 10 MeV. The fit yields a signal of 41 events over

a background of about 35 events, with a quoted significance of

7.8 σ. The observed width of 26 MeV is consistent with the

resolution.

The SAPHIR experiment — The 1997–1998 data from the

SAPHIR experiment [6], run at the ELSA facility in Bonn,

allow study of the reaction γp → nK+K0S, with an incident

tagged photon beam with energy between 0.9 and 2.6 GeV.

To enhance the Θ+ signal, a requirement that cos θcm > 0.5,

where θcm is the angle between the beam and the K0S in the

center of mass, is imposed. A signal of about 55 events over a

background of about 56 is observed in the nK+ mass spectrum

at a mass of 1540 ± 4 ± 2 MeV. The quoted significance is

4.8 σ, and the width is less than 25 MeV. Because there is no

significant signal in the pK+ spectrum observed in a separate

experiment to study γp → pK+K−, the authors conclude that

the Θ+ must have I = 0.

A compendium of neutrino experiments — Asratyan

et al. [7] have analyzed a database of some 120,000 ν and

ν charged-current events from the BEBC (CERN) and 15-foot

(Fermilab) bubble chambers; the fills were hydrogen, deuterium,

or neon. Some of the runs had mean incident energies of about

40 GeV and others about 110 GeV. The authors looked for

final states with a proton (momentum between 300 and 900

MeV/c), and a K0S decay, both originating from the same

vertex. The goal was to search for evidence of the Θ+ in the

pK0S mass spectra. A signal consisting of an excess of about

27 events over a background of about 8 events, at 1533 ± 5

MeV, was observed in the combined neon and deuterium data.

The quoted significance is 6.7 σ, and the width is less than 20

MeV. There is one concern here: the K0S can have S = +1 or

−1, and there are numerous S = −1 baryon resonances. The

authors argue that, since there is no established S = −1, I = 1

narrow resonance near 1530 MeV, the observed structure must

be taken as evidence for the Θ+.

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The HERMES experiment — In the HERMES experiment

[8], a 27.6 GeV positron beam from the HERA storage ring is

incident on a deuterium target in a search for Θ+ in quasi-real

inclusive photoproduction. The analysis selects final states with

a proton and K0S → π+π− decay. In the resulting pK0

S mass

spectrum, an enhancement at a mass of 1528±2.6±2.1 MeV is

observed. Depending on the background model, the significance

is said to be 4-to-6 σ and the width may be larger than expected

from just the measurement uncertainty of 4.3-to-6.2 MeV (one

standard deviation).

III. Information based on earlier data

There are a number of old experiments that may be relevant

to the search for a Θ+. We consider three sets of experiments:

(1) Studies of K+p and K+d interactions leading to KNπ

final states. One looks for an enhancement in nK+ and pK0

mass distributions.

(2) Studies of π−p interactions leading to KKN final states,

again looking for structure in the KN mass distributions.

(3) Measurements of K+d total and charge-exchange cross

sections as functions of incident momentum, looking for a cross

section peak in the neighborhood of 440 MeV/c.

K+p and K+d → KNπ — One might expect that an

S = +1 initial state would increase the likelihood of producing

an S = +1 resonance in the final state. Published results for

the reactions K+p → pK0π+, pK+π0, and nK+π+, studied

in bubble chambers at incident momenta of 960, 1200, 1210,

1290, 1360, 1380, 1520, 1585, 1690, and 2650 MeV/c [9–12],

have been examined with some care. In most cases, only Dalitz

plots are available, but Berthon et al. [12] also supplies pK0S

mass spectra with very substantial statistics. In these final

states, the K∗(892) and ∆(1232) dominate, and most features

of the KN spectra are simply reflections of these resonances.

Study of all the available Dalitz plots, especially away from the

known resonance bands, shows no indication of a population

increase near a pK0 or nK+ mass of 1540 MeV. Figure 3

shows some representative Dalitz plots, with the diagonal lines

corresponding to a 1540 MeV KN resonance. For a strongly

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Figure 3: Dalitz plots for K+N → KNπ reac-tions studied in hydrogen and deuterium bubblechambers. References, going clockwise startingat upper left, are [9], [9], [13], [12] and [12].The diagonal lines show where one would expectto see the Θ(1540)+.

decaying spin-1/2 state, the distribution of points along the

lines should be uniform.

The Berthon et al. pK0 mass spectra [12] show no indi-

cation of structure near 1540 MeV for incident momenta of

1210, 1290, 1380 MeV/c, but there is just a hint at 1690

MeV/c. Inspection of the corresponding Dalitz plot, however

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(see Fig. 3), indicates that any small population excess is likely

related to overlap with the K∗ resonance band. Similarly, the

K+d → KNπ(N) Dalitz plots (see Fig. 3) from Hirata et al.

[13] are also dominated by the same known resonance bands.

It is important to note that these bubble-chamber data have

no acceptance issue, and that they have not been subjected to

any cuts, unlike the claimed signal populations, where cuts have

been made that enhance the Θ+ signal relative to background.

π−p → nK+K− and pK0SK− — Dahl at al. [14] used the

Berkeley 72-in hydrogen bubble chamber to study the reactions

π−p → nK+K− and π−p → pK−K0S at momenta from 1.5

to 4.2 GeV/c. Their paper provides the relevant nK+ and

pK0S mass spectra, as well as Dalitz plots for three momentum

groupings: 1.6–2.3, 2.9–3.3, and 3.8–4.2 GeV/c. Of the six

relevant mass spectra, only one, nK+ at 3.8–4.2 GeV/c, has

the slightest hint of structure at low mass, but that structure is

actually centered at about 1600 MeV with a width of roughly

200 MeV. There is simply no evidence in these data for a narrow

KN resonance at 1540 MeV.

K+d cross section data — An I = 0 KN resonance should

manifest itself through increases in the K+n charge-exchange

and total cross sections at the resonance cm energy near 1540

MeV, corresponding for a neutron at rest to an incident K+

momentum of 442 MeV/c. Since free-neutron targets are not

available, K+d cross-section measurements are required, and

proper account must be taken of the Fermi momentum of the

bound neutron. The distribution of the Fermi momentum in

deuterium peaks near 50 MeV/c, and for a fixed incident K+

momentum leads to a cm energy distribution with a full width

of about 30 MeV. This number is, as shown below, much larger

than any reasonable estimate of the Θ+ width, and also is

larger than the typical spread of incident momentum at any

measurement point.

It is straightforward to calculate the resonance cross section

averaged over the Fermi momentum distribution, as determined

by the deuteron wave function. The result can be written as

σR = ABiBfΓ, where Bi and Bf are the initial and final Θ+

branching ratios relevant to the reaction under study, and Γ

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is the full width. The coefficient A is the product of several

factors, including the result of the Fermi-motion averaging

process. For an incident K+ momentum close to the resonant

value for a stationary neutron target (442 MeV/c), and for a

Θ+ having spin 1/2 and isospin 0, the value of A is 3.6 mb/MeV

[15].

We first apply this result to K+d charge exchange, K+d →

K0pp, using the measurements from Slater et al. [16] at incident

momenta of 376 and 530 MeV/c, and Damerell et al. [17] at 434,

526, and 604 MeV/c. The 434 MeV/c measurement is close to

the resonance value, and the others are sufficiently distant that,

even with the Fermi smearing, their resonance contributions are

small. We estimate the resonance part of the 434-MeV/c cross

section by subtracting from it a background estimated from

interpolations and extrapolations of the cross sections at the

other momenta. These subtractions yield numbers smaller than

the estimated errors of 0.3 mb. There is therefore no evidence

for a significant resonant contribution, and we estimate a

conservative upper limit for σR of 1 mb. Here Bi = Bf = 1/2

in the above formula, and we deduce an upper limit for Γ of 1.1

MeV.

A similar analysis can be applied to the K+d total cross

section, using the data of Bowen et al. [18] at 366, 440, and 506

MeV/c. The 440 MeV/c point is very close to the resonance

value, and the other two points are sufficiently distant to avoid

the inclusion of resonance contributions arising from Fermi

smearing. Subtraction of a linearly interpolated background

cross section from the measured value at 440 MeV/c leads to an

excess of 0.6±0.3 mb. The fact that this difference deviates from

zero should not be taken as evidence for the Θ+: it can simply

reflect deviation from linearity in the momentum dependence of

the cross section. We take 1.5 mb as a conservative upper limit

to the resonance cross section. Here Bi=1/2 and Bf =1, and

the upper limit on Γ is 0.8 MeV.

Finally, we consider the I = 0 KN total cross sections

reported by Bowen et al. [18] and Carroll et al. [19] at 440

MeV/c, and take the even more conservative approach of

considering the full cross section at that momentum as resonant.

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The Carroll and Bowen measurements disagree by about 3 mb,

and we use Carroll’s larger value of 13 mb. With Bi = Bf = 1,

the upper limit for Γ is 3.6 MeV.

These width limits are predicated on the Θ+ mass being in

the range of 1533–1543 MeV, corresponding closely to incident

momenta at which the K+d charge-exchange and total cross

sections have been measured. For masses of 1528 or 1548 MeV,

the upper limits would increase by a factor of 1.6.

IV. Width estimate from xenon experiment

The results of the DIANA xenon charge-exchange experi-

ment [4] have been analyzed by Cahn and Trilling [15] on the

assumption that, near the resonance, one is observing charge

exchange on a single nucleon. Associating the observed signal

and background populations with resonant and non-resonant

charge-exchange cross sections, they deduce a Θ+ width of

0.9 ± 0.3 MeV, where the quoted error is statistical. The sys-

tematic uncertainty is difficult to evaluate.

V. Results from partial-wave analysis

Motivated by the newly reported results, Arndt et al. [20]

have recently reanalyzed K+N scattering data in the 1540 MeV

cm energy region. They have considered possible structure not

only in the P01 partial wave, but also in other S, P, and D

waves. An immediate result was that the addition of resonances

of widths above 5 MeV resulted in an enormous increase in the

χ2 of their fit to data. Indeed, they found no χ2 improvement

in their fit from the addition of resonances in S, P, or D waves

unless the inserted structures had widths of 1 MeV or less.

They conclude that Θ+ widths larger than a few MeV are

excluded, but that the existence of a Θ+ in the P01 state with

a width of 1 MeV or less is possible. These results are stronger

than, although consistent with, a 6-MeV upper limit given by

Nussinov [21] and a 5-MeV limit by Haidenbauer and Krein

[22], and are consistent with the limits quoted in Secs. III and

IV above.

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VI. Comments on all these results

What can we conclude from these various results and

observations? One general principle should apply: For claims

of major new discoveries, the burden of proof is greater than

for research results that fall within the boundaries of what is

already established. Has this burden been met well enough to

claim the discovery of an exotic baryon resonance?

Measured in terms of claimed numbers of standard de-

viations, the results are impressive. In some cases [5, 6, 7],

inspection of the published plots suggests that the backgrounds

may be somewhat underestimated (background fits seem to

be normalized below the observed backgrounds), reducing per-

haps the real significance of the results. Nevertheless, there

are substantial indications that something interesting is be-

ing observed. However, that something seems to behave rather

differently from the known non-exotic resonances. As one ex-

ample, the Λ(1520) decays by D-wave to KN with a partial

width of 7.2 MeV, much larger than the upper limits based

on measured cross sections and partial-wave analyses for the

presumed P-wave Θ(1540)+.

There are some further concerns about the new evidence

for the Θ+. In most cases, the signal does not appear in a

significant way until various cuts are made, often reducing the

data sample by a large factor. Because all but the xenon and

neutrino experiments involve spectrometers of finite acceptance,

it is difficult for the reader of these papers to know what role

kinematics and reflections from other resonances may have

played in determining the results, especially since the cuts were

likely chosen to optimize observed signal to background.

One of the most powerful tools for understanding resonances

in three-body final states has been the use of Dalitz plots to

study correlations and reflections, yet there are no published

Dalitz plots in any of the new papers that involve three-body

final states [2, 3, 6]. The possible importance of reflections has

been emphasized in a recent paper by Dzierba et al. [23].

In three of the papers, the Θ+ production is from a nucleus

(carbon, xenon, or neon): the decay products may be created

inside the nucleus, and may further interact before leaving the

June 16, 2004 21:53

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nucleus, raising some uncertainties about the interpretation of

the final state. In short, most of the new papers are relatively

brief, and yet, given the potential importance of the results, the

work cries for more complete description and discussion.

There is the further problem that there seems to be no

evidence for the Θ+ in the rather extensive existing K+N

charge-exchange and total cross section data, in the KNπ

and KKN final states produced by incident kaons and pions

over a range of energies, and in the results of K+N partial

wave analyses. All the observations may be consistent with

a Θ+ having a width of 1 MeV or less, but then there are

two further questions: Why the very small width for a strong

decay, and why is the very narrow Θ+ so readily produced in

photoproduction experiments?

There is one other tantalizing piece of information. Alt

et al. [24] have recently claimed to see, at the 4 σ level, another

exotic baryon, an S = −2, Q = −2 ddssu state (see the lower

left corner of Fig. 1) decaying into Ξ−π− with a mass of

1862 ± 2 MeV and a width of less than 18 MeV. This mass

agrees with neither the Diakonov et al. prediction of 2070 MeV

[1] nor a later prediction of 1750 MeV from Jaffe and Wilczek

[25]. Nevertheless, this observation is additional support for the

existence of exotic baryons.

VII. Future Needs

What experiments do we need to establish fully the Θ+,

recognizing the fact that its width may be very small? One can

suggest two experiments:

(1) Confirmation with high statistics, much improved ef-

fective mass resolution, and excellent particle identification, of

the photoproduction results, through study of such reactions as

γp → nK+K0S, γn → pK0

SK−, and γn → nK+K−.

(2) Measurement in the 400–500 MeV/c incident momentum

range of the K+d → K0Sp(p) charge-exchange cross section as a

function of the final-state K0Sp mass. This requires measurement

of the K0S decay and reconstruction of the K0

Sp mass with

the best possible resolution, in order to demonstrate resonant

June 16, 2004 21:53

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behavior undiluted by target Fermi motion or beam-momentum

spread.

References

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21. S. Nussinov, hep-ph/0307357 (2003).

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24. C. Alt et al., Phys. Rev. Lett. 92, 042003 (2004).

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